By Andrew Putnis
The topic of mineralogy has moved clear of the systematic remedy of mineral teams towards the learn of the habit of minerals based on geological tactics. it will be significant that we comprehend the physics and chemistry of minerals as this reaction as a rule contains structural and chemical adjustments inside person minerals in addition to reactions among minerals. this can be the 1st textual content to supply an advent to trendy mineralogy for undergraduate scholars. the most, and infrequently advanced, ideas required to appreciate minerals and the approaches that ensue inside of them are awarded in a simple to persist with demeanour with none advanced mathematical remedy. The e-book offers with solid-state ameliorations in minerals, which happen according to alterations in temperature and strain, in addition to introducing the fundamental crystallography, physics and chemistry had to comprehend those methods. No wisdom of physics, chemistry and arithmetic past high-school point is thought.
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14. Examples of lattice planes and their Miller indices. — — •— — •— — •— — • A. 15. The orientation of (200) planes is the same as that of (100) planes, but the interplanar spacing of (200) planes is clearly one-half of the (100) interplanar spacing. The set of (200) planes includes all of the planes in this diagram whereas the set of (100) planes is shown by the darker lines. The bold square is the unit cell. e.  is not, in general, the direction normal to (123). The direction [UVW] in a lattice with unit cell base vectors a, b, c is a direction parallel to the vector Ua 4- Vb + We, where U,V,W are integers.
12. The E vibrations of the two refracted rays must lie at right angles within this elliptical section. The two principal axes of this elliptical section define the two vibration directions', and the lengths of the semimajor and semiminor axes of the ellipse define the two refractive indices. 12, the relevant elliptical section would contain the optic axis and the two refractive indices would be e and o. This section would have the maximum birefringence. e. zero birefringence). For any general direction in a uniaxial indicatrix, one of the refractive indices must always be o, while the other will have a value between e and o, and this is usually denoted e'.
Therefore, if for example a crystal has a 4-fold axis of symmetry, then the variation in the physical property must also obey the 4-fold axis. Expressed more formally, this is known as Neumann's Principle: the symmetry elements of any physical property of a crystal must include the symmetry elements of the point group of the crystal. We have already seen that we can describe second rank tensor properties by a representation ellipsoid even in the most general case, and as the ellipsoid has three mirror planes it therefore follows that the physical properties may have more symmetry than the crystal.